Question

write an equation in slope intercept form for a line that passes through the given point and is perpendicular to the graph of the equation.(3,-2); y = × + 4

Answer 1

We know that two lines are perpendicular if and only if their slopes fullfil:

`m_1m_2=-1`

Then we need to find the slope of the equation given:

`y=x+4`

we notice that this equation is written in the slope intercept form:

`y=mx+b`

comparing this equations we notice that:

`m_1=1`

Now, plugging this value in the condition and solving for the second slope we have:

`\begin{gathered} 1m_2=-1 \\ m_2=-(1)/(1) \\ m_2=-1 \end{gathered}`

Now that we have the slope of the line we are looking form we plug its value, and the point in the equation:

`y-y_1=m(x-x_1)`

then:

`\begin{gathered} y-(-2)=-1(x-3) \\ y+2=-x+3 \end{gathered}`

finally we write the equation in the slope intercept form given above:

`\begin{gathered} y+2=-x+3 \\ y=-x+3-2 \\ y=-x+1 \end{gathered}`

Therefore the equation we are looking for is:

`y=-x+1`